Usually an old VideoGame. One that is remembered by hoards of pasty faced geeks with fondness. I guess you could also include the really good modern games such as Q3 and the wonderful Half-Life too.
I would consider Quake to be a classic. Quake III isn't even close.
There are a few key terms which differentiate periods of VideoGameDevelopment?. These are common terms, and the exact dates vary somewhat.
Classic games must pass the same test as any classic. There's a reason why a Mustang is a classic but a Pinto isn't.
Cars are one of the poorest examples you can give, because there really are "hard definitions" of classic: for example, see http://www.dot10.state.pa.us/pdotforms/fact_sheets/fs-ant.pdf. Legally, a Pinto is a classic. On the other hand, I don't know of any video game aficionado who wouldn't consider, for example, MULE or Civilization or Balance of Power to be a "classic".